A008491 Expansion of (1-x^9 ) / (1-x)^9.

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24309, 43749, 75537, 125805, 202995, 318483, 487311, 729036, 1068705, 1537965, 2176317, 3032523, 4166175, 5649435, 7568955, 10027986, 13148685, 17074629, 21973545, 28040265, 35499915, 44611347, 55670823, 69015960

Offset

0,2

Comments

Growth series of the affine Weyl group of type A8. - Paul E. Gunnells, Jan 06 2017

References

R. Bott, The geometry and the representation theory of compact Lie groups, in: Representation Theory of Lie Groups, in: London Math. Soc. Lecture Note Ser., vol. 34, Cambridge University Press, Cambridge, 1979, pp. 65-90.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = n*(3044 + 1869*n^2 + 126*n^4 + n^6)/560 for n>0. - Colin Barker, Jan 06 2017

E.g.f.: 1 + x*(5040 + 7560*x + 5320*x^2 + 1610*x^3 + 266*x^4 + 21*x^5 + x^6)*exp(x)/560. - G. C. Greubel, Nov 07 2019

Maple

1, seq(n*(3044+1869*n^2+126*n^4+n^6)/560, n=1..40); # G. C. Greubel, Nov 07 2019

Mathematica

CoefficientList[Series[(1-x^9)/(1-x)^9, {x, 0, 35}], x] (* Harvey P. Dale, May 04 2014 *)

Prog

(PARI) Vec((1-x^9 )/(1-x)^9 + O(x^35)) \\ Colin Barker, Jan 06 2017
(Magma) [1] cat [n*(3044+1869*n^2+126*n^4+n^6)/560: n in [1..40]]; // G. C. Greubel, Nov 07 2019
(Sage) [1]+[n*(3044+1869*n^2+126*n^4+n^6)/560 for n in (1..40)] # G. C. Greubel, Nov 07 2019
(GAP) Concatenation([1], List([1..40], n-> n*(3044+1869*n^2+126*n^4+n^6)/560 )); # G. C. Greubel, Nov 07 2019

Crossrefs

Sequence in context: A341206 A306942 A289354 * A023034 A000581 A306939

Adjacent sequences: A008488 A008489 A008490 * A008492 A008493 A008494

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved